I currently have this.
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\begin{tikzpicture}[
cube/.style={very thick,black},
grid/.style={very thin,gray},
axis/.style={->,blue,thick}
]
%draw the axes
\draw[axis] (0,0,0) -- (6,0,0) node[anchor=west]{$y$};
\draw[axis] (0,0,0) -- (0,6,0) node[anchor=west]{$z$};
\draw[axis] (0,0,0) -- (0,0,6) node[anchor=west]{$x$};
%draw the top and bottom of the cube
\draw[cube] (0,0,0) -- (0,0,4) -- (4,0,4) -- (4,0,0) -- cycle;
\draw[axis] (2,0,2) -- (2,4,2) node[anchor=west]{$v$};
\end{tikzpicture}
Thanks,
Kevin